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Baris 157: hold for any angle {{mvar\|θ}} and any integer {{mvar\|k}}.--> == Nilai aljabar == {{Stub}} [[Berkas:Unit circle angles color.svg\|right\|thumb\|300px\|<!--The [[unit circle]], with some points labeled with their cosine and sine (in this order), and the corresponding angles in radians and degrees.-->]] [[Ekspresi aljabar]] untuk sudut terpenting adalah sebagai berikut: :<math>\sin 0 = \sin 0^\circ \quad= \frac{\sqrt0}2 = 0</math> ([[straight angle]]) :<math>\sin \frac\pi6 = \sin 30^\circ = \frac{\sqrt1}2 = \frac{1}{2}</math> :<math>\sin \frac\pi4 = \sin 45^\circ = \frac{\sqrt{2}}{2}</math> :<math>\sin \frac\pi3 = \sin 60^\circ = \frac{\sqrt{3}}{2}</math> :<math>\sin \frac\pi2 = \sin 90^\circ = \frac{\sqrt4}2 = 1</math> ([[right angle]]) Menulis pembilang sebagai akar kuadrat dari bilangan bulat non-negatif berurutan, dengan penyebut 2, memberikan cara mudah untuk mengingat nilai.<ref name="Larson_2013"/> Ekspresi sederhana seperti itu umumnya tidak ada untuk sudut lain yang merupakan kelipatan rasional dari sudut lurus. Untuk sudut yang diukur dalam derajat, merupakan kelipatan tiga, sinus dan cosinus dapat dinyatakan dalam [[akar kuadrat]],<!--see [[Trigonometric constants expressed in real radicals]]. These values of the sine and the cosine may thus be constructed by [[Compass-and-straightedge construction\|ruler and compass]]-->. <!--For an angle of an integer number of degrees, the sine and the cosine may be expressed in terms of [[square root]]s and the [[cube root]] of a non-real [[complex number]]. [[Galois theory]] allows proving that, if the angle is not a multiple of 3°, non-real cube roots are unavoidable. For an angle which, measured in degrees, is a [[rational number]], the sine and the cosine are [[algebraic number]]s, which may be expressed in terms of [[nth root\|{{mvar\|n}}th roots]]. This results from the fact that the [[Galois group]]s of the [[cyclotomic polynomial]]s are [[cyclic group\|cyclic]]. For an angle which, measured in degrees, is not a rational number, then either the angle or both the sine and the cosine are [[transcendental number]]s. This is a corollary of [[Baker's theorem]], proved in 1966.--> === Nilai aljabar sederhana === <!--The following table summarizes the simplest algebraic values of trigonometric functions.<ref name="Abramowitz and Stegun">Abramowitz, Milton and Irene A. Stegun, p. 74</ref> The symbol {{math\|∞}} represents the [[point at infinity]] on the [[projectively extended real line]]; it is not signed, because, when it appears in the table, the corresponding trigonometric function tends to {{math\|+∞}} on one side, and to {{math\|–∞}} on the other side, when the argument tends to the value in the table.--> :<math> \begin{array}{\|c\|ccccccccc\|} \hline \begin{matrix}\text{Radian}\\ \text{Sudut}\end{matrix} & \begin{matrix}0\\ 0^\circ\end{matrix} & \begin{matrix}\frac{\pi}{12}\\ 15^\circ\end{matrix} & \begin{matrix}\frac{\pi}{8}\\ 22.5^\circ\end{matrix} & \begin{matrix}\frac{\pi}{6}\\ 30^\circ\end{matrix} & \begin{matrix}\frac{\pi}{4}\\ 45^\circ\end{matrix} & \begin{matrix}\frac{\pi}{3}\\ 60^\circ\end{matrix} & \begin{matrix}\frac{3\pi}{8}\\ 67.5^\circ\end{matrix} & \begin{matrix}\frac{5\pi}{12}\\ 75^\circ\end{matrix} & \begin{matrix}\frac{\pi}{2}\\ 90^\circ\end{matrix} \\ \hline \sin & 0 & \frac{ \sqrt{6} - \sqrt{2} } {4} & \frac{ \sqrt{2 - \sqrt{2}} } {2} & \frac{1}{2} & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{2} & \frac{ \sqrt{2 + \sqrt{2}} } {2} & \frac{ \sqrt{6} + \sqrt{2} } {4} & 1 \\ \cos & 1 & \frac{\sqrt{6}+\sqrt{2}}{4} & \frac{ \sqrt{2 + \sqrt{2}} } {2} & \frac{\sqrt{3}}{2} & \frac{\sqrt{2}}{2} & \frac{1}{2} & \frac{ \sqrt{2 - \sqrt{2}} } {2} & \frac{ \sqrt{6} - \sqrt{2}} {4} & 0 \\ \tan & 0 & 2-\sqrt{3} & \sqrt{2} - 1 & \frac{\sqrt{3}}{3} & 1 & \sqrt{3} & \sqrt{2} + 1 & 2+\sqrt{3} & \infty \\ \cot & \infty & 2+\sqrt{3} & \sqrt{2} + 1 & \sqrt{3} & 1 & \frac{\sqrt{3}}{3} & \sqrt{2} - 1 & 2-\sqrt{3} & 0 \\ \sec & 1 & \sqrt{6} - \sqrt{2} & \sqrt{2} \sqrt{ 2 - \sqrt{2} } & \frac{2\sqrt{3}}{3} & \sqrt{2} & 2 & \sqrt{2} \sqrt{ 2 + \sqrt{2} } & \sqrt{6}+\sqrt{2} & \infty \\ \csc & \infty & \sqrt{6}+\sqrt{2} & \sqrt{2} \sqrt{ 2 + \sqrt{2} } & 2 & \sqrt{2} & \frac{2\sqrt{3}}{3} & \sqrt{2} \sqrt{ 2 - \sqrt{2} } & \sqrt{6} - \sqrt{2} & 1 \\\hline \end{array} </math> == Dalam kalkulus == == Identitas dasar ==

Fungsi trigonometri: Perbedaan antara revisi